We demonstrate that a magneto-convection simulation incorporating essential physical processes governing solar surface convection exhibits turbulent smallscale dynamo action. By presenting a derivation of the energy balance equation and transfer functions for compressible magnetohydrodynamics (MHD), we quantify the source of magnetic energy on a scale-by-scale basis. We rule out the two alternative mechanisms for the generation of small-scale magnetic field in the simulations: the tangling of magnetic field lines associated with the turbulent cascade and Alfvénization of small-scale velocity fluctuations ("turbulent induction"). Instead, we find the dominant source of small-scale magnetic energy is stretching by inertial-range fluid motions of small-scale magnetic field lines against the magnetic tension force to produce (against Ohmic dissipation) more small-scale magnetic field. The scales involved become smaller with increasing Reynolds number, which identifies the dynamo as a small-scale turbulent dynamo.

We quantify possible differences between turbulent dynamo action in the Sun and the dynamo action studied in idealized simulations. For this purpose, we compare Fourier-space shell-to-shell energy transfer rates of three incrementally more complex dynamo simulations: an incompressible, periodic simulation driven by random flow, a simulation of Boussinesq convection, and a simulation of fully compressible convection that includes physics relevant to the near-surface layers of the Sun. For each of the simulations studied, we find that the dynamo mechanism is universal in the kinematic regime because energy is transferred from the turbulent flow to the magnetic field from wavenumbers in the inertial range of the energy spectrum. The addition of physical effects relevant to the solar near-surface layers, including stratification, compressibility, partial ionization, and radiative energy transport, does not appear to affect the nature of the dynamo mechanism. The role of inertial-range shear stresses in magnetic field amplification is independent from outer-scale circumstances, including forcing and stratification. Although the shell-to-shell energy transfer functions have similar properties to those seen in mean-flow driven dynamos in each simulation studied, the saturated states of these simulations are not universal because the flow at the driving wavenumbers is a significant source of energy for the magnetic field.

We present direct numerical simulations and Lagrangian averaged (also known as α-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The α-model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The α model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed. PACS numbers: 47.27.Eq; 47.27.Gs; 47.11.+j The magnetohydrodynamic (MHD) approximation is often used to model plasmas or conducting fluids in astrophysical and geophysical environments. However, given the huge amount of temporal and spatial scales involved in the dynamics of these objects, simulations are always carried out in a region of parameter space far from the observed values. Lagrangian averaged magnetohydrodynamics (LAMHD), also called the MHD alpha-model [1, 2] (or the Camassa-Holm equations in early papers studying the hydrodynamic case [3]), has been recently introduced as a way to reduce the number of degrees of freedom of the system, while keeping accurate evolution for the large scales. This approach (as well as large eddy simulations, or LES, for MHD; see e.g. [4]) is intended to model astrophysical or geophysical flows at high Reynolds numbers using available computational resources. Several aspects of the MHD alpha-model have already been tested in two and three dimensions at moderate Reynolds numbers, against direct numerical simulations of the MHD equations [2]. These studies were focused on comparisons of the evolution of global quantities and the dynamics of the large scale components of the energy spectrum [2,5].All these models introduce changes in the small scales in order to preserve the evolution of the large scales. In several cases, it is of interest to know the statistics of the small scales. It is also important to model properly the small scales because they have an effect on large scales, as for example in the case of eddy noise: the beating of two small scales eddies produces energy at the large scale, and this may affect the global longtime evolution of the flow, an issue that arises in global climate evolution or in solar-terrestrial interactions. Moreover, plasmas and conducting fluids generate thin and intense current sheets where magnetic reconnection takes place. In these regions, the magnetic field and the current rapidly change sign, and after reconnection the magnetic energy is turned into mechanical and thermal energy. These events are known to take place in the magnetopause [6], the magnetotail [7], the solar atmosphere [8], and the interplanetary medium [9].Current sheets are strongly localized and intermittent. To preserve reliable statistics of these events in models of MHD turbulenc...